A neural network to learn the connection between two totally different type of images
I would try a pair of separate deep image embeddings with a contrastive loss. The idea is similar to the Siamese network architecture. In Siamese networks the pairs of images are of the same type - so both input images are fed through the copy of the same network. In your case the images are of different kinds, so I would just have separate nets for person images and fingerprints.